I am studying for a group theory exam which doubles as an introduction to category theory. In the chapter on abelian groups, we introduced the notion of a divisible group.
I consider the category $Ab_{div}$ of divisible abelian groups, this is a full subcategory of $Ab$, and as such there is a natural inclusion into $Ab$. Often times, we get interesting constructions/operations when considering adjoints of inclusions. For example if we consider $Ab_{tor}$ the category of abelian groups where every element is torsion, than the adjoint to the inclusion functor is the functor which sends $A$ to $T(A)$ its torsion subgroup.
Does the inclusion of $Ab_{div}$ into $Ab$ have an adjoint?